Department of Agricultural & Resource Economics, UCB

Transcription

1 Department of Agricultural & Resource Economics, UCB CUDARE Working Papers (University of California, Berkeley) Year 2005 Paper 996 A Simple Lagrange Multiplier F-Test for Multivariate Regression Models Timothy K. Beatty University of British Columbia Muzhe Yang University of California, Berkeley Jeffrey T. LaFrance University of California, Berkeley This paper is posted at the escholarship Repository, University of California. ucb/996 Copyright c 2005 by the authors.

2 A Simple Lagrange Multiplier F-Test for Multivariate Regression Models Abstract This paper proposes a straightforward, easy to implement approximate F- test which is useful for testing restrictions in multivariate regression models. We derive the asymptotics for our test statistic and investigate its finite sample properties through a series of Monte Carlo experiments. Both theory suggests and simulations confirm that our approach will result in strictly better inference than the leading alternative

3 Department of Agricultural & Resource Economics, UCB CUDARE Working Papers (University of California, Berkeley) Year 2005 Paper 996 A Simple Lagrange Multiplier F-Test for Multivariate Regression Models Timothy K. Beatty Jeffrey T. LaFrance University of British Columbia University of California, Berkeley Muzhe Yang University of California, Berkeley This paper is posted at the escholarship Repository, University of California. ucb/996 Copyright c 2005 by the authors.

4 A Simple Lagrange Multiplier F-Test for Multivariate Regression Models Abstract This paper proposes a straightforward, easy to implement approximate F- test which is useful for testing restrictions in multivariate regression models. We derive the asymptotics for our test statistic and investigate its finite sample properties through a series of Monte Carlo experiments. Both theory suggests and simulations confirm that our approach will result in strictly better inference than the leading alternative

5 DEPARTMENT OF AGRICULTURAL AND RESOURCE ECONOMICS AND POLICY DIVISION OF AGRICULTURAL AND NATURAL RESOURCES UNIVERSITY OF CALIFORNIA AT BERKELEY Working Paper No. 996 A SIMPLE LAGRANGE MULTIPLIER F-TEST FOR MULTIVARIATE REGRESSION MODELS by Timothy K. M. Beatty, Jeffrey T. LaFrance, and Muzhe Yang Copyright 2005 by Jeffrey T. LaFrance. All rights reserved. Readers may make verbatim copies of this document for noncommercial purposes by any means, provided that this copyright notice appears on all such copies. California Agricultural Experiment Station Giannini Foundation of Agricultural Economics February, 2005

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19 Figure 1. Empirical and True F(10,320) CDF Linear Model, Known True CDF for F(10,320) Empirical CDF for (NT-K) x LM / (G x SSR U ) Empirical CDF for (NT-K) x LM / (G x NT) F(x) x Figure 2. Empirical and True F(10,320) CDF Linear Model, Estimated True CDF for F(10,320) Empirical CDF for (NT-K) x LM / (G x SSR U ) Empirical CDF for (NT-K) x LM / (G x NT) F(x) x 14

20 Figure 3. Empirical and True F(10,320) CDF LinQuad Model, Known True CDF for F(10,320) Empirical CDF for (NT-K) x LM / (G x SSR U ) Empirical CDF for (NT-K) x LM / (G x NT) F(x) x Figure 4. Empirical and True F(10,320) CDF LinQuad Model, Estimated True CDF for F(10,320) Empirical CDF for (NT-K) x LM / (G x SSR U ) Empirical CDF for (NT-K) x LM / (G x NT) F(x) x 15

21 Figure 5. Empirical and True F(10,320) CDF Quadratic Utility, Known True CDF for F(10,320) Empirical CDF for (NT-K) x LM / (G x SSR U ) Empirical CDF for (NT-K) x LM / (G x NT) F(x) x Figure 6. Empirical and True F(10,320) CDF Quadratic Utility, Estimated True CDF for F(10,320) Empirical CDF for (NT-K) x LM / (G x SSR U ) Empirical CDF for (NT-K) x LM / (G x NT) F(x) x 16